The major purpose of this research is to develop new methods for the design and analysis of time to event data that are encountered in cancer research. Specifically, the following research questions will be considered. Many statistical models have been proposed to relate survival time to prognostic factors. Most of methods for estimating parameters in these models assume that the data are either exact or possibly right censored. Most often, however, the clinical event data from cancer clinical trials is only known to have occurred within an interval of time corresponding to clinic visits. This is called interval censored data. In this research proposal, methods for analyzing such interval censored will be studied extensively. The analysis of time dependent prognostic factors is very important in clinical research. The methods that have been proposed in the past assume that the time dependent data are measured continuously through time and without measurement error. In actuality, however, such data are measured only periodically with possible measurement error. Standard methods applied to such data will lead to biased results. In this research proposal, bias reduction techniques will be investigated. These methods will combine techniques in longitudinal data analysis together with methods for analyzing survival data. Finally methods for monitoring time to event endpoints in cancer clinical trials with more than two treatments will be developed. Specifically, sequential rules will be derived for eliminating inferior treatments as quickly as possible during interim monitoring while preserving the overall operating characteristics.